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Stochastic resonance in noisy maps as dynamical threshold-crossing systems
Matyjaskiewicz1, Holyst, Krawiecki
1Faculty of Physics, Warsaw University of Technology, Poland. matyjas@if.pw.edu.pl
Summary
Stochastic resonance is observed in both the logistic map and the kicked spin model when noise and periodic modulation interact. This phenomenon indicates enhanced signal-to-noise ratio due to transitions between symmetric states.
Area of Science:
- Nonlinear Dynamics
- Statistical Physics
- Complex Systems
Background:
- Investigates the interplay between noise and periodic modulation in dynamical systems.
- Focuses on the logistic map beyond the first bifurcation and the kicked spin model with Ising anisotropy and damping.
Purpose of the Study:
- To analyze the occurrence of stochastic resonance in two distinct complex systems.
- To understand how periodic modulation affects transition probabilities between symmetric states.
Main Methods:
- Theoretical analysis using adiabatic theory.
- Numerical simulations to validate analytical results.
- Examination of system dynamics under combined noise and periodic forcing.
Main Results:
- Both models exhibit two distinct symmetric states corresponding to different phases or attractors.
- Periodic modulation symmetrically influences transition probabilities between states.
- Stochastic resonance is observed in both systems, characterized by an optimal signal-to-noise ratio.
Conclusions:
- The logistic map and kicked spin model behave as threshold-crossing systems with internal dynamics.
- Stochastic resonance is a robust phenomenon in these systems, driven by noise and periodic modulation.
- Adiabatic theory provides a qualitatively accurate framework for understanding these dynamics.